Changes in images of brain functional activity that are produced by disease or by activation of various pathways in the normal brain can only be unambiguously interpreted if the rates of the physiological and biochemical processes that underlie the imaging method are quantified. In imaging modalities that use radioactive tracers, e.g. positron emission tomography (PET), quantification is carried out by means of a mathematical model that describes the rates of the biochemical reactions in the metabolic pathway of the tracer and traced molecules. Selection of the best kinetic model is critical as the use of an inappropriate model can lead to substantial errors in quantification and possible misinterpretation of results. Once a model is selected, numerical procedures that are efficient, robust, and require minimal assumptions about the errors in the measurements are required to estimate accurately the parameters. Additionally, powerful statistical tests are needed so that the data can be examined for significant differences among experimental groups. The objective of this project is to develop better techniques for addressing these interrelated mathematical and statistical issues; advances in the current year were made in the following areas:(1) Work concluded on the development of a robust minimum variance adaptive (MVA) method for parameter estimation and statistical hypothesis testing. Rather than choosing a specific estimator or test statistic prior to the data analysis, the MVA method adapts to each data set by choosing from a large candidate group the single best (minimum variance) estimator or test statistic for the particular data. Unlike parametric methods, the MVA method requires no prior assumptions about the statistical probability distribution of the underlying population. (2) Examination of the effects of the diffusion limitation of water, and of kinetic heterogeneity of tissues necessarily included in field of view of PET measurements, on determinations of cerebral blood flow (CBF) with O-15 labeled water and PET continued. The kinetic model currently used for measurement of CBF does not take either effect into account. We have previously quantified the extent to which kinetic heterogeneity leads to an underestimation of CBF with the kinetic model currently in use, and developed an alternative kinetic model that takes into account the heterogeneity and avoids the CBF underestimation. Due to the high degree of nonlinearity of the model in its parameters, however, estimation of the parameters with standard nonlinear least squares algorithms lacks robustness and is computationally intensive. We have developed an alternative algorithm that is both efficient and robust. Preliminary results from simulation studies indicate that the algorithm provides accurate estimates of weighted average blood flow and gray matter blood flow in a mixed tissue. Publications: Turkheimer F, Pettigrew K, Sokoloff L, Schmidt K (1999) "A minimum variance adaptive technique for parameter estimation and hypothesis testing," Commun Statist - Simula 28(4): 931-956.Turkheimer F, Pettigrew K, Sokoloff L, Smith CB, Schmidt K (2000) "Selection of an adaptive test statistic for use with multiple comparison analyses of neuroimaging data," Neuroimage 12(2): 219-229.Schmidt KC (2000) "Identification of linear compartmental systems that can be analyzed by spectral analysis of the sum of all compartments", in Physiological Imaging of the Brain with PET. A Gjedde, SB Hansen, GM Knudsen, OB Paulson, Eds. Academic Press (In press).